Vertical ground motion analysis for submerged pore-elastic media with random void ratios

Recently, very strong vertical ground motions have been recorded during several earthquakes. The vertical motions are the consequence of compressional stresses which are mainly transmitted by pore fluids. For linear elastic analysis of a submerged soil layer, the permeability has a very minor effect on shear-wave response for which pore fluids are not taken into account. But on compressional-wave response, the permeability dominates the damping effect and is thought as the principal influential factor from pore fluids. In this study, the effect of changing permeability on damping is explored. In practice it is harder to obtain the coefficient of permeability, κ, than to measure the void ratio, e. In order to evaluate the permeability and explore its influence on vertical shaking, the formula relating κ–e for the saturated soil is selected for a 1D submerged pore-elastic model subjected to vertical sine-wave loading. The random, linear, linear-plus-random, logarithmic, and log-plus-random depth functions of void ratio are taken into account in this study. The intrinsic error due to the use of the arithmetic mean of permeability for a certain area with a heterogeneous distribution of permeability has also been assessed. Numerical simulations show that the five depth distributions of void ratio all result in the extra viscous forces. The damping effect on vertical shaking is mainly controlled by the harmonic mean of permeability and spatial distribution of permeability rather than the arithmetic mean of permeability. The harmonic mean is more appropriate than the arithmetic mean to be the representative permeability, because the damping coefficient is inversely proportional to permeability.